Mobile Apps latest technologies research

I am currently on a research understanding the whole buzz around some technologies that claim that they deploy themselves as cross-platform apps once you write your code in HTML5/CSS3/AngularJS/Whatever client side techonology. I understand those technologies provide you with a bridge to the native-side of the OS you are running on, but I still lack some real important information regarding them.

1. Do all those PhoneGap/Ionic/Cordova just wrap your client-side code into an application? Is it the same as using the web-browser to get to a URL but with only some native-like additions(Camera/File etc..).
2. Do those technologies just connect to your website that is online using DNS? Or is the "Website" you are building does not sit on a server but only on the local OS? Can they run that application offline?
3. Besides the native additions you get with those kind of technologies, why bother developing with them when you can on the other hand develop a responsive website that can also work on desktop?
4. Can you connect to a server-side using Ionic/Phonegap? Let's say I have an MS-SQL Table I want to communicate with- is that possible?

I really have a hard time understanding what all those technologies are any good. Still, it is growing in popularity. Thanks for any light on that matter.